Browse Questions

# $18$ mice were placed in two experimental groups and one control group,with all groups equally large.In how many ways can the mice be placed into three groups?

$\begin{array}{1 1}(A)\;17153136\\(B)\;170848\\(C)\;1767532\\(D)\;\text{None of these}\end{array}$

Total no of mice =18
Total no of groups =3
The groups are equally large hence each group can have =6 mice
Hence the total no of ways in which the mice can be placed =18!
Since the possible no of ways the mice can be placed in each group $\Rightarrow 6!$
Hence the total no of ways in which the mice can be placed into three groups are =$\large\frac{18!}{6!\times 6!\times 6!}$
$\Rightarrow \large\frac{18\times 17\times 16\times 15\times 14\times 13\times 12\times 11\times 10\times 9\times 8\times 7\times 6!}{6\times 5\times 4\times 3\times 2\times 1\times 6\times 5\times 4\times 3\times 2\times 1\times 6!}$
$\Rightarrow 17153136$
Hence (A) is the correct answer.